Eigenmodes

In this system we can "see" the eigenvalues as the squared frequencies of the
eigenmodes. One can also see the eigenmodes.
1) Starting with an initial
condition where bi=0 and a2=0, we have a double pendulum
where both pendula swing parallel. The spring strenght does not matter and the
penduli move as if they were not connected.
2) Starting with an initial condition
where bi=0 and a1=0, the pendulum swing against each other.
The frequency (1+2c)1/2 has become slightly larger.

The first eigenmode.

The second eigenmode. It swings a bit faster. The
small spring strength makes it swing only slightly faster.